an:07183751
Zbl 1436.53074
Jordan, Joshua; Streets, Jeffrey
On a Calabi-type estimate for pluriclosed flow
EN
Adv. Math. 366, Article ID 107097, 18 p. (2020).
00448179
2020
j
53E30 35K55
complex geometry; non-K??hler; pluriclosed flow; generalized complex geometry
Summary: The regularity theory for pluriclosed flow hinges on obtaining \(C^\alpha\) regularity for the metric assuming uniform equivalence to a background metric. This estimate was established in [14] by an adaptation of ideas from Evans-Krylov, the key input being a sharp differential inequality satisfied by the associated `generalized metric' defined on \(T \oplus T^\ast\). In this work we give a sharpened form of this estimate with a simplified proof. To begin we show that the generalized metric itself evolves by a natural curvature quantity, which leads quickly to an estimate on the associated Chern connections analogous to, and generalizing, Calabi-Yau's \(C^3\) estimate for the complex Monge-Amp??re equation.